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  3. Bäcklund and Darboux Transformations
  • Cited by 531
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    • Publisher:
      Cambridge University Press
      Publication date:
      04 March 2010
      24 June 2002
      ISBN:
      9780511606359
      9780521813310
      9780521012881
      DOI:
      https://doi.org/10.1017/CBO9780511606359
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.712kg, 432 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.596kg, 432 Pages
      • Subjects:
      Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics, Mathematical Modeling and Methods
      Series:
      Cambridge Texts in Applied Mathematics (30)
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    Subjects:
    Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics, Mathematical Modeling and Methods
    Series:
    Cambridge Texts in Applied Mathematics (30)
    Information

    Book description

    This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for use at a higher undergraduate or graduate level for applied mathematicians or mathematical physics.

    Reviews

    'It is an excellent book for graduate students and young researchers … very useful for scientists in this field.'

    Source: Nieuw Archief voor Wiskunde

    'The book certainly is a recommendable book for everyone who is interested in these transformations as well as in the related geometry and modern applications.'

    Source: Bulletin of the Belgian Mathematical Society

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